中文摘要：

分形理论在地理空间信息的复杂性分析中具有广泛的应用前景,但是强调完全自相似为基础的单一分形维数,难以描述复杂变化的地理目标特征.本文研究表明,与分形维数相比,M-R曲线所包含的更丰富的地理空间特征信息使之成为更值得关注的分形分析对象.在此基础上,本文初步阐述了M-R曲线的性质与地理空间意义,并进一步探讨了M-R曲线的扩展分析方法,包括M-R曲线的函数拟合与分维谱分析.最后以小比例尺地图中河流数据为例,分析了我国长江、黄河两大河流的空间形态特征及其规律.实验表明,在小尺度范围内长江具有更丰富的细节变化,黄河则在更大的尺度上表现出复杂性.

英文摘要：

Fractal theory will have a wide application in the field of the complexity analysis of geographic spatial information, but it is difficult to describe the characteristic of geographic objects by means of the single fractal dimension method, which emphasizes on the absolute self-similarity. This paper showed that, being compared with the single fractal dimension, the M-R curve comprises more abundant characteristic information of geographic spatial details, so it should be considered as a more important fractal analysis object. On the basis of the above analysis, firstly, this paper primarily introduced the characteristic and the geographical spatial significance of M-R curve; secondly, several extended analysis methods for M-R curve were further discussed, including the functional simulation of M-R curve, the establishment and analysis of fractal dimension spectrum; and finally, selecting the river data on small scale map as experimental data, this paper analyzed the spatial morphologic character and discipline between two great rivers in China, viz. the Yangtze River and the Yellow River. The experiment indicated that the Yangtze River has more complicated detailed change in the scope of small scales, and the Yellow River has more obvious complexity in the larger ones.